Part of the book series:Lecture Notes in Computer Science ((LNIP,volume 7432))
Included in the following conference series:
2870Accesses
Abstract
We present an algorithm to generate an interpolation or approximation model consisting of many patches from a triangle mesh, and each patch is a weighted combination of the three surfaces associated with the vertices of a triangle. Moreover, to make the whole surface include fewer patches, mesh simplification is introduced into the process of surface construction. The algorithm takes a triangle mesh and a given error as input, and iteratively deletes vertex whose distance to the surface model constructed from the simplified mesh is less than or equal to the given error until convergence. Since the method is based on surface approximation and vertex deletion, it allows us to control the error between the generated model and the original mesh precisely. Furthermore, many experimental results show that the generated models approximate the original models well.
This is a preview of subscription content,log in via an institution to check access.
Access this chapter
Subscribe and save
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Buy Now
- Chapter
- JPY 3498
- Price includes VAT (Japan)
- eBook
- JPY 5719
- Price includes VAT (Japan)
- Softcover Book
- JPY 7149
- Price includes VAT (Japan)
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bajaj, C.L., Ihm, I.: Algebraic surface design with hermite interpolation. ACM Transactions on Graphics 11, 61–69 (1992)
Bajaj, C., Ihm, I., Warren, J.: Higher-order interpolation and least-squares approximation using implicit algebraic surfaces. ACM Transactions on Graphics 12, 327–347 (1993)
Subaihi, I., Watson, G.: Algebraic ftting of quadric surfaces to data. Commun. Appl. Anal., 539–548 (2005)
Yan, D.-M., Liu, Y., Wang, W.: Quadric Surface Extraction by Variational Shape Approximation. In: Kim, M.-S., Shimada, K. (eds.) GMP 2006. LNCS, vol. 4077, pp. 73–86. Springer, Heidelberg (2006)
Savchenko, V., Pasko, E.A., Okunev, O.G., Kunii, T.L.: Function representation of solids reconstructed from scattered surface points and contours. Computer Graphics Forum 12, 181–188 (1995)
Turk, G., Brien, J.F.: Shape transformation using variational implicit functions. In: Proceedings of ACM SIGGRAPH, pp. 335–342 (1999)
Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C., Evans, T.R.: Reconstruction and representation of 3d objects with radial basis functions. In: Proceedings of ACM SIGGRAPH, pp. 67–76 (2001)
Turk, G., Brien, J.F.O.: Modelling with implicit surfaces that interpolate. ACM Transactions on Graphics 21, 855–873 (2002)
Yngve, G., Turk, G.: Robust creation of implicit surfaces from polygonal meshes. IEEE Transactions on Visualization and Computer Graphics 8, 346–359 (2002)
Muraki, S.: Volumetric shape description of range data using blobby model. In: Proceedings of ACM SIGGRAPH, pp. 67–76 (1991)
Morse, B., Yoo, T.S., Rheingans, P., Chen, D.T., Subramanian, K.: Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions. In: Proceedings of Shape Modelling International, pp. 89–98 (2001)
Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., Seidel, H.P.: Multi-level partition of unity implicits. ACM Transactionson Graphics 22, 463–470 (2003)
Shen, C., Brien, J.F., Shewchuk, J.R.: Interpolating and approximating implicit surfaces from polygon soup. ACM Transactions on Graphics 23 (2004)
Beardsley, P.: Pose estimation of the human head by modelling with an ellipsoid. In: Proc. of IEEE Conf. on Automatic Face Gesture Recognition, Nara (1998)
Fitzgibbon, A., Pilu, M., Fisher, R.B.: Direct least square ftting of ellipses. IEEE Transaction on Pattern Analysis and Machine Intelligence 21, 476–480 (1999)
Li, Q., Griffiths, J.: Least squares ellipsoid specific fitting. In: Proc. of the IEEE CS GMP, pp. 335–340 (April 2004)
Allaire, S., Jacq, J.J., Burdin, V., Couture, C.: Type-constrained robust fitting of quadrics with application to the 3d morphological characterization of saddle-shaped articular surfaces. In: IEEE 11th International Conference on Computer Vision, ICCV 2007, pp. 1–8 (2007)
Dai, M., Newman, T.S., Cao, C.: Least-squares-based fitting of paraboloids. Pattern Recogniyion 40, 504–515 (2007)
Benk, P., Ks, G., Vrady, T., Andor, L., Marin, R.: Constrained fitting in reverse engineering. Computer Aided Geometric Design 19, 173–205 (2002)
Vanco, M., Hamann, B., Brunnett, G.: Surface reconstruction from unorganized point data with quadrics. Computer Graphics Forum 27, 1593–1606 (2008)
Schroeder, W.J., Zarge, J.A., Lorensen, W.E.: Decimation of triangle meshes. Computers Graphics 25, 175–184 (1991)
Garland, M., Heckbert, P.: Surface simplification using quadric error metrics. In: Proceedings of SIGGRAPH 1997, ACM Press ACM SIGGRAPH, Computer Graphics Proceedings. Annual Conference Series, pp. 209–216. ACM (1997)
Gao, S.-S., Zhang, C.-M., Zhong, L.: Interpolation by Piecewise Quadric Polynomial to Scattered Data Points. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Remagnino, P., Nefian, A., Meenakshisundaram, G., Pascucci, V., Zara, J., Molineros, J., Theisel, H., Malzbender, T. (eds.) ISVC 2006. LNCS, vol. 4292, pp. 106–115. Springer, Heidelberg (2006)
Blane, M.M., Lei, Z., Civi, H., Cooper, D.B.: The 3l algorithm for fitting implicit polynomial curves and surfaces to data. IEEE Transactions on Pattern Analysis and Machine Intelligence 22, 298–313 (2000)
Tasdizen, T., Tarel, J., Cooper, D.: Improving the stability of algebraic curves for applications. IEEE Transactions on Image Processing 9, 405–416 (2000)
Helzer, A., Barzohar, M., Malah, D.: Stable fitting of 2d curves and 3d surfaces by implicit polynomials. IEEETransactions on Pattern Analysis and Machine Intelligence 26, 1283–1294 (2004)
Garland, M., Willmott, A., Heckbert, P.S.: Hierarchical face clustering on polygonal surfaces. In: Proc. ACM Symposium on Interactive 3D Graphics 2001, pp. 49–58. ACM Press, New York (2001)
Steiner, D.C., Alliez, P., Desbrun, M.: Variational shape approximation. ACM Transactions on Graphics 23, 905–914 (2004)
Takashi, K., Yutaka, O., Kiwamu, K.: Hierarchical error-driven approximation of implicit surfaces from polygonal meshes. In: Proceedings of the Symposium on Geometry Processing, vol. 256, pp. 21–30 (2006)
Cazals, F., Pouget, M.: Topology driven algorithms for ridge extraction on meshes. Technical Report RR-5526, INRIA (2005)
Baldonado, M., Chang, C.C., Gravano, L., Paepcke, A.: The stanford digital library metadata architecture. Int. J. Digit. Libr. 1, 108–121 (1997)
Author information
Authors and Affiliations
School of Computer Science and Technology, Shandong University, Jinan, China
Weitao Li, Yuanfeng Zhou, Li Zhong, Xuemei Li & Caiming Zhang
Shandong Province Key Lab of Digital Media Technology, Shandong University of Finance and Economics, Jinan, China
Caiming Zhang
- Weitao Li
You can also search for this author inPubMed Google Scholar
- Yuanfeng Zhou
You can also search for this author inPubMed Google Scholar
- Li Zhong
You can also search for this author inPubMed Google Scholar
- Xuemei Li
You can also search for this author inPubMed Google Scholar
- Caiming Zhang
You can also search for this author inPubMed Google Scholar
Editor information
Editors and Affiliations
Department of Computer Science, University of Nevada, 89557, Reno, NV, USA
George Bebis
NASA Ames Research Center, 94035, Moffett Field, CA, USA
Richard Boyle
Lawrence Berkeley National Laboratory, 94720, Berkeley, CA, USA
Bahram Parvin
Desert Research Institute, 89512, Reno, NV, USA
Darko Koracin
Department of Computer Science, University of California at Irvine, 92697-3435, Irvine, CA, USA
Charless Fowlkes
Eastman Kodak Company, 14650-2102, Rochester, NY, USA
Sen Wang
Department of Computer Science and Engineering, University of Colorado at Denver, 80217, Denver, CO, USA
Min-Hyung Choi
VRVis Zentrum für Virtual Reality and Visualisierung, 1220, Vienna, Austria
Stephan Mantler
California Institute for Telecommunications and Information Technology, University of California,,, San Diego, 92093, La Jolla, CA, USA
Jürgen Schulze
KAUST Visualizatioin Core Lab., 23955-6900, Thurwal, Saudi Arabia
Daniel Acevedo
Stony Brook University, 11794-4400, NY, USA
Klaus Mueller
Argonne National Laboratory, 60439, IL, USA
Michael Papka
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, W., Zhou, Y., Zhong, L., Li, X., Zhang, C. (2012). Surface Construction with Fewer Patches. In: Bebis, G.,et al. Advances in Visual Computing. ISVC 2012. Lecture Notes in Computer Science, vol 7432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33191-6_71
Download citation
Publisher Name:Springer, Berlin, Heidelberg
Print ISBN:978-3-642-33190-9
Online ISBN:978-3-642-33191-6
eBook Packages:Computer ScienceComputer Science (R0)
Share this paper
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative